It is currently 25 Feb 2018, 19:47

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# Is m + z > 0 (1) m - 3z > 0 (2) 4z - m > 0

Author Message
TAGS:

### Hide Tags

Intern
Joined: 11 Jun 2010
Posts: 13
Is m + z > 0 (1) m - 3z > 0 (2) 4z - m > 0 [#permalink]

### Show Tags

16 Dec 2010, 09:24
6
KUDOS
59
This post was
BOOKMARKED
00:00

Difficulty:

55% (hard)

Question Stats:

67% (00:41) correct 33% (00:57) wrong based on 1179 sessions

### HideShow timer Statistics

Is m + z > 0

(1) m - 3z > 0
(2) 4z - m > 0
[Reveal] Spoiler: OA
Math Expert
Joined: 02 Sep 2009
Posts: 43917
Is m + z > 0 (1) m - 3z > 0 (2) 4z - m > 0 [#permalink]

### Show Tags

16 Dec 2010, 09:29
31
KUDOS
Expert's post
33
This post was
BOOKMARKED
Is m+z > 0

(1) m - 3z > 0. Insufficient on its own.

(2) 4z - m > 0. Insufficient on its own.

$$(m-3z)+(4z-m)>0$$;

$$z>0$$, so $$z$$ is positive.

From (1) $$m>(3z=positive)$$, so $$m$$ is positive too ($$m$$ is more than some positive number $$3z$$, so it's positive). Therefore, $$m+z=positive+positive>0$$. Sufficient.

For graphic approach refer to: http://gmatclub.com/forum/is-m-z-0-1-m- ... 75657.html
_________________
Intern
Joined: 24 Nov 2010
Posts: 5
Re: Is m + z > 0 (1) m - 3z > 0 (2) 4z - m > 0 [#permalink]

### Show Tags

17 Dec 2010, 09:13
1
KUDOS
smitakokne wrote:
Is m+z > 0

1. m-3z > 0
2. 4z-m > 0

OA : C

Need help in underdstanding how we arrive at C.

Bunuel,

is m+z > 0 the same as m/z > -1 ?

if so, then 1. would be m/z > 3, which is SUFF
and 2. would be m/z < 4, which is INSUFF

so I would have said A

Please correct me if I'm wrong - my inequality skills are a bit rusty
Math Expert
Joined: 02 Sep 2009
Posts: 43917
Re: Is m + z > 0 (1) m - 3z > 0 (2) 4z - m > 0 [#permalink]

### Show Tags

17 Dec 2010, 09:25
5
KUDOS
Expert's post
2
This post was
BOOKMARKED
psirus wrote:
smitakokne wrote:
Is m+z > 0

1. m-3z > 0
2. 4z-m > 0

OA : C

Need help in underdstanding how we arrive at C.

Bunuel,

is m+z > 0 the same as m/z > -1 ?

if so, then 1. would be m/z > 3, which is SUFF
and 2. would be m/z < 4, which is INSUFF

so I would have said A

Please correct me if I'm wrong - my inequality skills are a bit rusty

No, it's not correct.

When you are writing m/z>-1 from m+z>0 you are actually dividing both parts of inequality by z: never multiply or reduce (divide) inequality by an unknown (a variable) unless you are sure of its sign since you do not know whether you must flip the sign of the inequality.

So if we knew that z>0 then m+z>0 --> m/z+1>0 and if we knew that z<0 then m+z>0 --> m/z+1<0.

Hope it's clear.
_________________
Manager
Joined: 02 Oct 2010
Posts: 142
Re: Is m + z > 0 (1) m - 3z > 0 (2) 4z - m > 0 [#permalink]

### Show Tags

19 Jan 2011, 22:14
Bunuel wrote:
smitakokne wrote:
Is m+z > 0

1. m-3z > 0
2. 4z-m > 0

OA : C

Need help in underdstanding how we arrive at C.

(1) m - 3z > 0. Insufficient on its own.
(2) 4z - m > 0. Insufficient on its own.

(1)+(2) Remember we can add inequalities with the sign in the same direction --> $$m-3z+4z-m>0$$ --> $$z>0$$, so $$z$$ is positive. From (1) $$m>3z=positive$$, so $$m$$ is positive too ($$m$$ is more than some positive number $$3z$$, so it's positive) --> $$m+z=positive+positive>0$$. Sufficient.

Hello Bunnel,

As you said in the above post..
what should we have different signs...
Math Expert
Joined: 02 Sep 2009
Posts: 43917
Re: Is m + z > 0 (1) m - 3z > 0 (2) 4z - m > 0 [#permalink]

### Show Tags

20 Jan 2011, 02:19
4
KUDOS
Expert's post
2
This post was
BOOKMARKED
jullysabat wrote:
Bunuel wrote:
smitakokne wrote:
Is m+z > 0

1. m-3z > 0
2. 4z-m > 0

OA : C

Need help in underdstanding how we arrive at C.

(1) m - 3z > 0. Insufficient on its own.
(2) 4z - m > 0. Insufficient on its own.

(1)+(2) Remember we can add inequalities with the sign in the same direction --> $$m-3z+4z-m>0$$ --> $$z>0$$, so $$z$$ is positive. From (1) $$m>3z=positive$$, so $$m$$ is positive too ($$m$$ is more than some positive number $$3z$$, so it's positive) --> $$m+z=positive+positive>0$$. Sufficient.

Hello Bunnel,

As you said in the above post..
what should we have different signs...

You can only add inequalities when their signs are in the same direction:

If $$a>b$$ and $$c>d$$ (signs in same direction: $$>$$ and $$>$$) --> $$a+c>b+d$$.
Example: $$3<4$$ and $$2<5$$ --> $$3+2<4+5$$.

You can only apply subtraction when their signs are in the opposite directions:

If $$a>b$$ and $$c<d$$ (signs in opposite direction: $$>$$ and $$<$$) --> $$a-c>b-d$$ (take the sign of the inequality you subtract from).
Example: $$3<4$$ and $$5>1$$ --> $$3-5<4-1$$.
_________________
Senior Manager
Joined: 24 Mar 2011
Posts: 428
Location: Texas
Re: Is m + z > 0 (1) m - 3z > 0 (2) 4z - m > 0 [#permalink]

### Show Tags

26 May 2011, 10:10
4
KUDOS
1
This post was
BOOKMARKED
Plus in arbitary values to check is m+z is always greater than 0 or there are other possibilities

st-1 ==> m - 3z >0
m =1 and z = -1 ==> m+z = 0
m=2 and z = -1 ==> m+z >0
not sufficient

st-2 ==> 4z-m>0
m = -1 and z = 0.1 ==> m+z < 0
m=2 and z = 1 ==> m+z >0
not sufficient

combining both

m-3z + 4z -m >0
z > 0.... (P)
from 1, m > 3z and from 2, 4z > m
==> 3z < m < 4z... (Q)
from (P) and (Q) m+Z > 0

Last edited by agdimple333 on 26 May 2011, 11:13, edited 1 time in total.
Manager
Joined: 14 Apr 2011
Posts: 192
Re: Is m + z > 0 (1) m - 3z > 0 (2) 4z - m > 0 [#permalink]

### Show Tags

26 May 2011, 11:07
2
KUDOS
Wow - Thank you agdimple333. That was quick and clear!

I was combining both to get that 3z < m < 4z but I did not add them to get that z > 0 as well. Now that I think again if m lies between 3z and 4z, then by this equation alone z has to be GT 0 because there is NO z < 0 that will ever satisfy this equation. Thanks again.
_________________

Looking for Kudos

Manager
Joined: 07 Jun 2011
Posts: 66
Re: Is m + z > 0 (1) m - 3z > 0 (2) 4z - m > 0 [#permalink]

### Show Tags

11 Aug 2011, 04:27
Brunel, could you help me to figure out where I am wrong.

From statement 1: M-3Z > 0

Adding 3Z to both sides of inequality

M>3Z

is Z is negative, then 3 times that negative number is definitely less than that number

for example Z = -.25

3Z = -.75 < Z

Z = -1
3Z = - 3 < Z

Zero does not apply because, then both sides would be equal.

Since we its evident that both Z and M are positive Z+M is greater than zero...

Where am I going wrong with my reasoning?
Math Forum Moderator
Joined: 20 Dec 2010
Posts: 1945
Re: Is m + z > 0 (1) m - 3z > 0 (2) 4z - m > 0 [#permalink]

### Show Tags

11 Aug 2011, 07:27
manishgeorge wrote:
Brunel, could you help me to figure out where I am wrong.

From statement 1: M-3Z > 0

Adding 3Z to both sides of inequality

M>3Z

is Z is negative, then 3 times that negative number is definitely less than that number

for example Z = -.25

3Z = -.75 < Z

Z = -1
3Z = - 3 < Z

Zero does not apply because, then both sides would be equal.

Since we its evident that both Z and M are positive Z+M is greater than zero...

Where am I going wrong with my reasoning?

m>3z
m=0; z=-1; m>3z; m+z=-1<0
m=1; z=0; m>3z; m+z=1>0
m=+1; z=-1; m>3z; m+z=0

Thus, knowing that m>3z is not sufficient to find whether m+z>0
Not Sufficient.
_________________
Director
Status: Done with formalities.. and back..
Joined: 15 Sep 2012
Posts: 634
Location: India
Concentration: Strategy, General Management
Schools: Olin - Wash U - Class of 2015
WE: Information Technology (Computer Software)
Re: Is m + z > 0 (1) m - 3z > 0 (2) 4z - m > 0 [#permalink]

### Show Tags

21 Nov 2012, 19:34
1
KUDOS
arvindbhat1887 wrote:
Is m+z>0?

(1) m > 3z
(2) m < 4z.

The answer is given as (C) Both statements together.
I don't understand how. Can someone please explain?
I think the answer is (E) Not sufficient with both
(1) tells you that m > 3z (2) tells you that m < 4z. Either of the two cases taken individually is not sufficient. So Rule out (A), (B), (D)
Therefore, 3z<m<4z when you combine the two.
Now z can take both -ve and +ve values. So, m + z can be either -ve or +ve depending on the value of z. Hence, (E).

Stem 1: m>3z
or m-3z >0
doesnt tell us anything about m+z. Not sufficient.

Stem 2: m<4z
or m-4z <0
or 4z-m >0
tells us nothing again. Not sufficient.

combining, we get that 3z <m <4z
also, if we add both equations,
m-3z >0
4z-m >0

we get, z>0
Thus since m>3z
=> m is also >0

therefore m+z >0
Sufficient.

Ans C it is.
_________________

Lets Kudos!!!
Black Friday Debrief

Director
Joined: 29 Nov 2012
Posts: 853
Re: Is m + z > 0 (1) m - 3z > 0 (2) 4z - m > 0 [#permalink]

### Show Tags

21 Jul 2013, 01:29
Bunuel wrote:

(1) m - 3z > 0. Insufficient on its own.
(2) 4z - m > 0. Insufficient on its own.

(1)+(2) Remember we can add inequalities with the sign in the same direction --> $$m-3z+4z-m>0$$ --> $$z>0$$, so $$z$$ is positive. From (1) $$m>3z=positive$$, so $$m$$ is positive too ($$m$$ is more than some positive number $$3z$$, so it's positive) --> $$m+z=positive+positive>0$$. Sufficient.

For graphic approach refer to: is-m-z-0-1-m-3z-0-2-4z-m-75657.html

I have one question when statements are combined, I got till the part z > 0 now I got confused here since in statement 1 I could prove it m>3z ( m is positive) but didn't how to apply z>0 to the second statement >>> 4z - m > 0

So when you reach that stage you can apply it to any of the statement and conclude its sufficient or you have to conclude using both statement separately?
_________________

Click +1 Kudos if my post helped...

Amazing Free video explanation for all Quant questions from OG 13 and much more http://www.gmatquantum.com/og13th/

GMAT Prep software What if scenarios http://gmatclub.com/forum/gmat-prep-software-analysis-and-what-if-scenarios-146146.html

Math Expert
Joined: 02 Sep 2009
Posts: 43917
Re: Is m + z > 0 (1) m - 3z > 0 (2) 4z - m > 0 [#permalink]

### Show Tags

21 Jul 2013, 01:37
1
KUDOS
Expert's post
fozzzy wrote:
Bunuel wrote:

(1) m - 3z > 0. Insufficient on its own.
(2) 4z - m > 0. Insufficient on its own.

(1)+(2) Remember we can add inequalities with the sign in the same direction --> $$m-3z+4z-m>0$$ --> $$z>0$$, so $$z$$ is positive. From (1) $$m>3z=positive$$, so $$m$$ is positive too ($$m$$ is more than some positive number $$3z$$, so it's positive) --> $$m+z=positive+positive>0$$. Sufficient.

For graphic approach refer to: is-m-z-0-1-m-3z-0-2-4z-m-75657.html

I have one question when statements are combined, I got till the part z > 0 now I got confused here since in statement 1 I could prove it m>3z ( m is positive) but didn't how to apply z>0 to the second statement >>> 4z - m > 0

So when you reach that stage you can apply it to any of the statement and conclude its sufficient or you have to conclude using both statement separately?

You got that m is positive with (1), so can stop there. If you combine you get that 4z>m>3z>0.
_________________
Senior Manager
Joined: 07 Apr 2012
Posts: 441
Re: Is m + z > 0 (1) m - 3z > 0 (2) 4z - m > 0 [#permalink]

### Show Tags

24 Nov 2013, 08:10
Bunuel wrote:
smitakokne wrote:
Is m+z > 0

1. m-3z > 0
2. 4z-m > 0

OA : C

Need help in underdstanding how we arrive at C.

(1) m - 3z > 0. Insufficient on its own.
(2) 4z - m > 0. Insufficient on its own.

(1)+(2) Remember we can add inequalities with the sign in the same direction --> $$m-3z+4z-m>0$$ --> $$z>0$$, so $$z$$ is positive. From (1) $$m>3z=positive$$, so $$m$$ is positive too ($$m$$ is more than some positive number $$3z$$, so it's positive) --> $$m+z=positive+positive>0$$. Sufficient.

For graphic approach refer to: is-m-z-0-1-m-3z-0-2-4z-m-75657.html

Hi Bunuel,

When I took both statements and in my head made the stipulations, I ended up with
3z<m<4z, but that did not yield the right answer.
Can you tell me what I am missing doing this vs. actually adding the equations?
Math Expert
Joined: 02 Sep 2009
Posts: 43917
Re: Is m + z > 0 (1) m - 3z > 0 (2) 4z - m > 0 [#permalink]

### Show Tags

24 Nov 2013, 08:13
1
KUDOS
Expert's post
ronr34 wrote:
Bunuel wrote:
smitakokne wrote:
Is m+z > 0

1. m-3z > 0
2. 4z-m > 0

OA : C

Need help in underdstanding how we arrive at C.

(1) m - 3z > 0. Insufficient on its own.
(2) 4z - m > 0. Insufficient on its own.

(1)+(2) Remember we can add inequalities with the sign in the same direction --> $$m-3z+4z-m>0$$ --> $$z>0$$, so $$z$$ is positive. From (1) $$m>3z=positive$$, so $$m$$ is positive too ($$m$$ is more than some positive number $$3z$$, so it's positive) --> $$m+z=positive+positive>0$$. Sufficient.

For graphic approach refer to: is-m-z-0-1-m-3z-0-2-4z-m-75657.html

Hi Bunuel,

When I took both statements and in my head made the stipulations, I ended up with
3z<m<4z, but that did not yield the right answer.
Can you tell me what I am missing doing this vs. actually adding the equations?

You missed the last step: from 3z<4z it follows that z>0, thus 3z=positive --> (3z=positive)<m --> m=positive --> m+z=positive.
_________________
Manager
Joined: 18 Jul 2013
Posts: 69
Location: Italy
GMAT 1: 600 Q42 V31
GMAT 2: 700 Q48 V38
Re: Is m + z > 0 (1) m - 3z > 0 (2) 4z - m > 0 [#permalink]

### Show Tags

23 Jul 2014, 12:15
Is that correct?

1) $$m-3z>0$$ <=> $$m>3z$$ Insuff
2) $$4z-m>0$$ <=> $$m<4z$$ Insuff

1+2)
we multiply 1) by 4, $$4m>12z$$
we multiply 2) by 3, $$3m<12z$$ <=> $$-3m>-12z$$

As we can add two inequalities $$4m-3m>0$$ so $$m>0.$$

from1), $$m>3z$$
from 2), $$m<4z$$ <=> $$-m>-4z$$

As we can add two inequalities $$0>-z$$ so $$z>0$$

so $$m+z>0$$
Math Expert
Joined: 02 Sep 2009
Posts: 43917
Re: Is m + z > 0 (1) m - 3z > 0 (2) 4z - m > 0 [#permalink]

### Show Tags

23 Jul 2014, 17:03
1
KUDOS
Expert's post
oss198 wrote:
Is that correct?

1) $$m-3z>0$$ <=> $$m>3z$$ Insuff
2) $$4z-m>0$$ <=> $$m<4z$$ Insuff

1+2)
we multiply 1) by 4, $$4m>12z$$
we multiply 2) by 3, $$3m<12z$$ <=> $$-3m>-12z$$

As we can add two inequalities $$4m-3m>0$$ so $$m>0.$$

from1), $$m>3z$$
from 2), $$m<4z$$ <=> $$-m>-4z$$

As we can add two inequalities $$0>-z$$ so $$z>0$$

so $$m+z>0$$

Yes, that's correct.

_________________
Intern
Joined: 28 Sep 2012
Posts: 12
Re: Is m + z > 0 (1) m - 3z > 0 (2) 4z - m > 0 [#permalink]

### Show Tags

07 Sep 2014, 07:41
Hi Bunuel, I have a doubt in this question. it is asked whether m+z>0 this implies that is m>-z?

Statement 1 says: m-3Z>0 then m>3z and 3z is definitely greater than -z then isnt m>-z. Please clarify.
Math Expert
Joined: 02 Sep 2009
Posts: 43917
Re: Is m + z > 0 (1) m - 3z > 0 (2) 4z - m > 0 [#permalink]

### Show Tags

07 Sep 2014, 07:56
snehamd1309 wrote:
Hi Bunuel, I have a doubt in this question. it is asked whether m+z>0 this implies that is m>-z?

Statement 1 says: m-3Z>0 then m>3z and 3z is definitely greater than -z then isnt m>-z. Please clarify.

3z is not always greater than -z. It's only true when z is positive, but if z is negative, then 3z < -z.
_________________
Retired Moderator
Joined: 29 Oct 2013
Posts: 282
Concentration: Finance
GPA: 3.7
WE: Corporate Finance (Retail Banking)
Re: Is m + z > 0 (1) m - 3z > 0 (2) 4z - m > 0 [#permalink]

### Show Tags

23 Dec 2015, 17:17
Bunuel, Skywalker18, Engr2012, and other experts :

Do you think algebraic approach works even if an answer choice is E in such similar questions? Or do we have to resort to graphic approach/number picking then? Any tips on how to attack these questions in general?

Thanks
_________________

My journey V46 and 750 -> http://gmatclub.com/forum/my-journey-to-46-on-verbal-750overall-171722.html#p1367876

Re: Is m + z > 0 (1) m - 3z > 0 (2) 4z - m > 0   [#permalink] 23 Dec 2015, 17:17

Go to page    1   2    Next  [ 30 posts ]

Display posts from previous: Sort by